{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Practical 5: Supervised Learning \n",
    "\n",
    "\n",
    "Upon completion of this session you should be able to:\n",
    "- understand data dependency, linear regression and distances.\n",
    "- be able to apply linear regression in Python.\n",
    "\n",
    "---\n",
    "- Materials in this module include resources collected from various open-source online repositories.\n",
    "- Jupyter source file can be downloaded from https://github.com/gaoshangdeakin/SIT384-Jupyter\n",
    "- If you found any issue/bug for this document, please submit an issue at [https://github.com/gaoshangdeakin/SIT384/issues](https://github.com/gaoshangdeakin/SIT384/issues)\n",
    "\n",
    "\n",
    "---\n",
    "\n",
    "\n",
    "\n",
    "This practical session will demonstrate different coefficient and linear regression.\n",
    "\n",
    "\n",
    "## Background\n",
    "\n",
    "### Machine Learning \n",
    "\n",
    "### Part 1 Data Dependency\n",
    "\n",
    "1.1 [Pearson's-r Correlation coefficient](#pearson)\n",
    "\n",
    "1.2 [Spearman's rank coefficient](#spearman)\n",
    "\n",
    "\n",
    "### Part 2 Linear Regression\n",
    "\n",
    "2.1 [Multiple Linear Regression](#mlr)\n",
    "\n",
    "2.2 [Regression for Median House Price](#rmhp)\n",
    "\n",
    "### Part 3 Distances\n",
    "\n",
    "3.1 [Euclidean Distance](#euclidean)\n",
    "\n",
    "3.2 [Cosine Distance](#cosine)\n",
    "\n",
    "3.3 [Term-by-Document Matrix](#t2d)\n",
    "\n",
    "\n",
    "## Tasks\n",
    "\n",
    "## Summary\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <span style=\"color:#0b486b\">Machine Learning</span>\n",
    "\n",
    "<a id = \"machinelearning\"></a>\n",
    "\n",
    "Machine learning (ML) is \"Machines imitating and adapting human like behavior\". In other words, we try to teach machines to “Learn from Experience”.\n",
    "\n",
    "Machine learning algorithms use computational methods to “learn” information directly from data without relying on a predetermined equation as a model. The algorithms adaptively improve their performance as the number of samples available for learning increases. The ML-Algorithms find natural patterns within the data, get insights and predict the unknown for better decisions.\n",
    "\n",
    "There are basically two types of ML Techniques:\n",
    "\n",
    "   1. Supervised Learning\n",
    "   2. Unsupervised Learning\n",
    "\n",
    "###Supervised Learning:\n",
    "\n",
    "Finds patterns (and develops predictive models) using both, input data and output data. All Supervised Learning techniques area form of either Classification or Regression.\n",
    "\n",
    "* Classification: used for predicting discrete responses.E.g. Whether India will WIN or LOSE a Cricket match? Whether an email is SPAM or GENUINE? WIN, LOSE, SPAM, GENUINE are the predefined classes. And output has to fall among these depending on the input.\n",
    "* Regression: used for predicting continuous responses.E.g. Trend in stock market prices, Weather forecast, etc.\n",
    "\n",
    "###Unsupervised Learning:\n",
    "\n",
    "Finds patterns based only on input data. This technique is useful when you’re not quite sure what to look for. Often used for exploratory Analysis of raw data. Most Unsupervised Learning techniques are a form of Cluster Analysis.\n",
    "\n",
    "* Cluster Analysis: you group data items that have some measure of similarity based on characteristic values. At the end what you will have is a set of different groups (Let’s assume A — Z such groups). A Data Item(d1) in one group(A) is very much similar to other Data Items(d2 — dx) in the same group(A), but d1 is significantly different from Data Items belonging to different groups (B — Z).\n",
    "\n",
    "SciPy and Scikit-Learn will be used in machine learning. For a quick review, go [.html version](practical5-review.html) or [.ipynb version](https://github.com/gaoshangdeakin/SIT384-Jupyter/blob/master/practical5-review.ipynb).  \n",
    "\n",
    "Before introducing regression, let's talk about data dependency first. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## <span style=\"color:#0b486b\">1. Data Dependency</span>\n",
    "\n",
    "<a id = \"pearson\"></a>\n",
    "\n",
    "\n",
    "### <span style=\"color:#0b486b\">1.1 Pearson's-r Correlation coefficient</span>\n",
    "\n",
    "The Pearson product-moment correlation coefficient is a measure of the strength of the linear relationship between two variables. The symbol for Pearson's correlation is \"ρ\" when it is measured in the population and \"r\" when it is measured in a sample. More detail can be found [statistics.laerd.com](https://statistics.laerd.com/statistical-guides/pearson-correlation-coefficient-statistical-guide.php) or [wikipedia.org](https://en.wikipedia.org/wiki/Pearson_correlation_coefficient).\n",
    "\n",
    "We assume $X=\\left\\{ X_{1},\\ldots,X_{n}\\right\\}$ \n",
    "and $Y=\\left\\{ Y_{1},\\ldots,Y_{n}\\right\\}$. Then Pearson-r correlation coefficient is defined as \n",
    "\n",
    "$$ \\rho(X,Y) = \\frac{\\text{cov}(X,Y)}{\\sigma_X \\sigma_Y} =  \\frac{\\sum_{i=1}^n (X_i - \\bar{X})(Y_i - \\bar{Y})}{\\sqrt{\\sum_{i=1}^n(X_i-\\bar{X})^2} \\sqrt{\\sum_{i=1}^n(Y_i-\\bar{Y})^2}} $$\n",
    "\n",
    "Use the car data and find the Pearson's-r correlation coefficient between car weights and fuel consumption."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import csv\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats\n",
    "import pandas as pd\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: wget in c:\\users\\shang\\appdata\\local\\continuum\\anaconda3\\lib\\site-packages (3.2)\n"
     ]
    }
   ],
   "source": [
    "#No need to use wget if you've retrieved file from clouddeakin.\n",
    "!pip install wget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r",
      "  0% [                                                                                ]    0 / 1167\r",
      "100% [................................................................................] 1167 / 1167"
     ]
    }
   ],
   "source": [
    "import wget\n",
    "\n",
    "link_to_data = 'https://raw.githubusercontent.com/gaoshangdeakin/SIT384/master/Auto.csv'\n",
    "DataSet = wget.download(link_to_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv('Auto.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Model</th>\n",
       "      <th>miles</th>\n",
       "      <th>cylinder number</th>\n",
       "      <th>Engine displacement</th>\n",
       "      <th>Horse power</th>\n",
       "      <th>Weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>Mazda RX4</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>160.0</td>\n",
       "      <td>110</td>\n",
       "      <td>2.620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>Mazda RX4 Wag</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>160.0</td>\n",
       "      <td>110</td>\n",
       "      <td>2.875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>Datsun 710</td>\n",
       "      <td>22.8</td>\n",
       "      <td>4</td>\n",
       "      <td>108.0</td>\n",
       "      <td>93</td>\n",
       "      <td>2.320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>Hornet 4 Drive</td>\n",
       "      <td>21.4</td>\n",
       "      <td>6</td>\n",
       "      <td>258.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>Hornet Sportabout</td>\n",
       "      <td>18.7</td>\n",
       "      <td>8</td>\n",
       "      <td>360.0</td>\n",
       "      <td>175</td>\n",
       "      <td>3.440</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               Model  miles  cylinder number  Engine displacement  \\\n",
       "0          Mazda RX4   21.0                6                160.0   \n",
       "1      Mazda RX4 Wag   21.0                6                160.0   \n",
       "2         Datsun 710   22.8                4                108.0   \n",
       "3     Hornet 4 Drive   21.4                6                258.0   \n",
       "4  Hornet Sportabout   18.7                8                360.0   \n",
       "\n",
       "   Horse power  Weight  \n",
       "0          110   2.620  \n",
       "1          110   2.875  \n",
       "2           93   2.320  \n",
       "3          110   3.215  \n",
       "4          175   3.440  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>miles</th>\n",
       "      <th>cylinder number</th>\n",
       "      <th>Engine displacement</th>\n",
       "      <th>Horse power</th>\n",
       "      <th>Weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>count</td>\n",
       "      <td>32.000000</td>\n",
       "      <td>32.000000</td>\n",
       "      <td>32.000000</td>\n",
       "      <td>32.000000</td>\n",
       "      <td>32.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mean</td>\n",
       "      <td>20.090625</td>\n",
       "      <td>6.187500</td>\n",
       "      <td>230.721875</td>\n",
       "      <td>146.687500</td>\n",
       "      <td>3.217250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>std</td>\n",
       "      <td>6.026948</td>\n",
       "      <td>1.785922</td>\n",
       "      <td>123.938694</td>\n",
       "      <td>68.562868</td>\n",
       "      <td>0.978457</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>min</td>\n",
       "      <td>10.400000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>71.100000</td>\n",
       "      <td>52.000000</td>\n",
       "      <td>1.513000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>25%</td>\n",
       "      <td>15.425000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>120.825000</td>\n",
       "      <td>96.500000</td>\n",
       "      <td>2.581250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>50%</td>\n",
       "      <td>19.200000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>196.300000</td>\n",
       "      <td>123.000000</td>\n",
       "      <td>3.325000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>75%</td>\n",
       "      <td>22.800000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>326.000000</td>\n",
       "      <td>180.000000</td>\n",
       "      <td>3.610000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>max</td>\n",
       "      <td>33.900000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>472.000000</td>\n",
       "      <td>335.000000</td>\n",
       "      <td>5.424000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           miles  cylinder number  Engine displacement  Horse power     Weight\n",
       "count  32.000000        32.000000            32.000000    32.000000  32.000000\n",
       "mean   20.090625         6.187500           230.721875   146.687500   3.217250\n",
       "std     6.026948         1.785922           123.938694    68.562868   0.978457\n",
       "min    10.400000         4.000000            71.100000    52.000000   1.513000\n",
       "25%    15.425000         4.000000           120.825000    96.500000   2.581250\n",
       "50%    19.200000         6.000000           196.300000   123.000000   3.325000\n",
       "75%    22.800000         8.000000           326.000000   180.000000   3.610000\n",
       "max    33.900000         8.000000           472.000000   335.000000   5.424000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Model</th>\n",
       "      <th>miles</th>\n",
       "      <th>cylinder number</th>\n",
       "      <th>Engine displacement</th>\n",
       "      <th>Horse power</th>\n",
       "      <th>Weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>Mazda RX4</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>160.0</td>\n",
       "      <td>110</td>\n",
       "      <td>2.620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>Mazda RX4 Wag</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>160.0</td>\n",
       "      <td>110</td>\n",
       "      <td>2.875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>Datsun 710</td>\n",
       "      <td>22.8</td>\n",
       "      <td>4</td>\n",
       "      <td>108.0</td>\n",
       "      <td>93</td>\n",
       "      <td>2.320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>Hornet 4 Drive</td>\n",
       "      <td>21.4</td>\n",
       "      <td>6</td>\n",
       "      <td>258.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>Hornet Sportabout</td>\n",
       "      <td>18.7</td>\n",
       "      <td>8</td>\n",
       "      <td>360.0</td>\n",
       "      <td>175</td>\n",
       "      <td>3.440</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               Model  miles  cylinder number  Engine displacement  \\\n",
       "0          Mazda RX4   21.0                6                160.0   \n",
       "1      Mazda RX4 Wag   21.0                6                160.0   \n",
       "2         Datsun 710   22.8                4                108.0   \n",
       "3     Hornet 4 Drive   21.4                6                258.0   \n",
       "4  Hornet Sportabout   18.7                8                360.0   \n",
       "\n",
       "   Horse power  Weight  \n",
       "0          110   2.620  \n",
       "1          110   2.875  \n",
       "2           93   2.320  \n",
       "3          110   3.215  \n",
       "4          175   3.440  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "miles = data['miles']\n",
    "weights = data['Weight']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "miles[:10]: 0    21.0\n",
      "1    21.0\n",
      "2    22.8\n",
      "3    21.4\n",
      "4    18.7\n",
      "5    18.1\n",
      "6    14.3\n",
      "7    24.4\n",
      "8    22.8\n",
      "9    19.2\n",
      "Name: miles, dtype: float64\n",
      "weights[:10]: 0    2.620\n",
      "1    2.875\n",
      "2    2.320\n",
      "3    3.215\n",
      "4    3.440\n",
      "5    3.460\n",
      "6    3.570\n",
      "7    3.190\n",
      "8    3.150\n",
      "9    3.440\n",
      "Name: Weight, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(\"miles[:10]:\", miles[:10])\n",
    "print(\"weights[:10]:\", weights[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pearson_r: -0.8676593765172278\n"
     ]
    }
   ],
   "source": [
    "pearson_r = np.cov(miles, weights)[0, 1] / (miles.std() * weights.std())\n",
    "print(\"pearson_r:\", pearson_r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        , -0.86765938],\n",
       "       [-0.86765938,  1.        ]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(miles,weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "horse = data['Horse power']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.65874789],\n",
       "       [0.65874789, 1.        ]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(weights,horse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1d0e23acfc8>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting\n",
    "fig, ax = plt.subplots(figsize=(7, 5), dpi=100)\n",
    "\n",
    "#s: marker size; color: marker color; alpha: marker opacity.\n",
    "#e.g. ax.scatter(x, y, s=10)\n",
    "#https://problemsolvingwithpython.com/06-Plotting-with-Matplotlib/06.10-Scatter-Plots/\n",
    "ax.scatter(weights,miles, alpha=0.6, edgecolor='none', s=100)\n",
    "ax.set_xlabel('Car Weight (tons)')\n",
    "ax.set_ylabel('Miles Per Gallon')\n",
    "\n",
    "#numpy.polyfit(x, y, deg, rcond=None, full=False, w=None, cov=False)\n",
    "#Fit a polynomial p(x) = p[0] * x**deg + ... + p[deg] of degree deg to points (x, y). \n",
    "#Returns a vector of coefficients p that minimises the squared error in the order deg, deg-1, … 0.\n",
    "#https://docs.scipy.org/doc/numpy/reference/generated/numpy.polyfit.html\n",
    "line_coef = np.polyfit(weights, miles, 1)\n",
    "xx = np.arange(1, 5, 0.1)\n",
    "yy = line_coef[0]*xx + line_coef[1]\n",
    "\n",
    "ax.plot(xx, yy, 'r', lw=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 1**: \n",
    "\n",
    "1. Find the Pearson's-r coefficient for two linearly dependent variables. Add some noise and see the effect of varying the noise. \n",
    "2. Simulate and visualize some data with positive linear correlation\n",
    "3. Simulate and visualize some data with negative linear correlation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.8712665124461638, 4.712293243757288e-32)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx = np.arange(-5, 5, 0.1)\n",
    "pp = 1.5  # level of noise\n",
    "yy = xx + np.random.normal(0, pp, size=len(xx))\n",
    "\n",
    "# visualize the data\n",
    "#plt.subplots() Plt.subplots(nrows, ncols) \n",
    "#The function returns a figure object and a tuple containing axes objects equal to nrows*ncols. \n",
    "#Each axes object is accessible by its index. \n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(xx, yy, c='r', edgecolor='none')\n",
    "ax.set_xlabel('X data')\n",
    "ax.set_ylabel('Y data')\n",
    "\n",
    "line_coef = np.polyfit(xx, yy, 1)\n",
    "line_xx = np.arange(-5, 5, 0.1)\n",
    "line_yy = line_coef[0]*line_xx + line_coef[1]\n",
    "\n",
    "#https://stackoverflow.com/questions/43482191/matplotlib-axes-plot-vs-pyplot-plot\n",
    "#plt.plot() can also be used\n",
    "#ax.plot(x, y, color='green', marker='o', linestyle='dashed', linewidth=2, markersize=12)\n",
    "#https://matplotlib.org/3.2.1/api/_as_gen/matplotlib.axes.Axes.plot.html\n",
    "ax.plot(line_xx, line_yy, 'b', lw=2)\n",
    "\n",
    "print (scipy.stats.pearsonr(xx, yy))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pearson's r coefficient is limited to analyze the linear correlation between two variables. It is not capable to show the non-linear dependency. Investigate the Pearson's r coefficient between two variables that are correlated non-linearly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '$Y = X^2+\\\\epsilon$')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate some data, first for X\n",
    "xx = np.arange(-5, 5, 0.1)\n",
    "\n",
    "# assume Y = 2Y + some perturbation\n",
    "pp = 1.1  # level of noise\n",
    "yy = xx**2 + np.random.normal(0, pp, size=len(xx))\n",
    "\n",
    "# visualize the data\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(xx, yy, c='r', edgecolor='b')\n",
    "ax.set_xlabel('X data')\n",
    "ax.set_ylabel('Y data')\n",
    "ax.set_title('$Y = X^2+\\epsilon$', size=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Pearson's-r correlation is near zero which means there is no linear correlation. But how about non-linear correlation? Isn't $y=x^2$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.       , -0.0348772],\n",
       "       [-0.0348772,  1.       ]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(xx,yy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id = \"spearman\"></a>\n",
    "\n",
    "\n",
    "### <span style=\"color:#0b486b\">1.2 Spearman's rank coefficient</span>\n",
    "\n",
    "Spearman's rank coefficient is used for discrete/ordinal data. Find the Spearman's rank between horse power and number of cylinders of the car data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Model</th>\n",
       "      <th>miles</th>\n",
       "      <th>cylinder number</th>\n",
       "      <th>Engine displacement</th>\n",
       "      <th>Horse power</th>\n",
       "      <th>Weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>Mazda RX4</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>160.0</td>\n",
       "      <td>110</td>\n",
       "      <td>2.620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>Mazda RX4 Wag</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>160.0</td>\n",
       "      <td>110</td>\n",
       "      <td>2.875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>Datsun 710</td>\n",
       "      <td>22.8</td>\n",
       "      <td>4</td>\n",
       "      <td>108.0</td>\n",
       "      <td>93</td>\n",
       "      <td>2.320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>Hornet 4 Drive</td>\n",
       "      <td>21.4</td>\n",
       "      <td>6</td>\n",
       "      <td>258.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>Hornet Sportabout</td>\n",
       "      <td>18.7</td>\n",
       "      <td>8</td>\n",
       "      <td>360.0</td>\n",
       "      <td>175</td>\n",
       "      <td>3.440</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               Model  miles  cylinder number  Engine displacement  \\\n",
       "0          Mazda RX4   21.0                6                160.0   \n",
       "1      Mazda RX4 Wag   21.0                6                160.0   \n",
       "2         Datsun 710   22.8                4                108.0   \n",
       "3     Hornet 4 Drive   21.4                6                258.0   \n",
       "4  Hornet Sportabout   18.7                8                360.0   \n",
       "\n",
       "   Horse power  Weight  \n",
       "0          110   2.620  \n",
       "1          110   2.875  \n",
       "2           93   2.320  \n",
       "3          110   3.215  \n",
       "4          175   3.440  "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SpearmanrResult(correlation=0.9017909351708425, pvalue=1.8676856258444694e-12)\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmUAAAG4CAYAAAAEx5BLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAgAElEQVR4nOzdeZxkd13v/9enep2lu2efyWTWJJNJQvY9MZCAAQQ0GIOCXmS9IlyUi169GPXn7s0FARUEUa4Ywg4iKhAhEkgI2chK9nW2zL53z9b79/dHVc/U9HRXV1VXd51Jv56Px3lM1znfU/Wpb9d0v/t7zvmeSCkhSZKk+srVuwBJkiQZyiRJkjLBUCZJkpQBhjJJkqQMMJRJkiRlgKFMkiQpAwxlkiRJGdBY7wImW0QEsBjYV+9aJEnSlNEGbE4lJoidcqGMfCDbWO8iJEnSlLME2DTaxqkYyvYBvPDCC7S3t9e7FkmS9CLX1dXF0qVLYYyjdFMxlAHQ3t5uKJMkSZnhif6SJEkZYCiTJEnKAEOZJElSBhjKJEmSMsBQJkmSlAGGMkmSpAwwlEmSJGWAoUySJCkDpuzksdJU1t3bz/ee3M6O/T005IJTF7Rx6clz613WqJ7fsZ971uyiu3eAma2NvHz1Aha0tx7V5hsPbuTRTZ0MpsTijmn86mUrmNbcUKeKS+vuG+CZbfs40DNAU0OwbM70Y95POdbvOsC2rh5SSrRPa+LUhW005KLm9W7pPMSmPYfoG0i0tTayauFMWhpr37fF3+e2aU284rT5zJtZeb+MR1d3H89t309P3yAtTTlOnj+TjmlNk1qDJs/mvYfYvPfIZ3v1ojaaGuo3XhUl7ov5ohQR7UBnZ2enM/prytl7sJd/uH0NP3puBwd7B4/atrC9hdedfQL/7ZLldaruWHc8u4Mv3ruBZ7fvp/hHVUMOzlk6i7deupRvPLyF7z6+ja5DfUft29yY46IVc/jTa85gQfu0Sa58ZJ0H+/jB09t5+IW99PQf3f8nzZvBS0+dx2mLSv9cSilx37o93PX8TrZ19Ry1ra21kYtWzOGlq+bR2jT+0PTYpk5+9NxO1u86eNT61qYc5y2bzctXz6etdfyB5fant/OlH2/guR0Hjvo+N+aCc5Z28I6fWslpJ0zsz+tNew9x29PbeWJzF4NFNeQCzljczlWrF3DirGx8jjR+j2zcyx3P7mTjnkNHrZ/W1MAFy2dz5er5zGyp3bhVV1cXHR0dAB0ppa7R2hnKpCliy95D/NZXH2bHvt6S7S5cMZsbrj2TXK6+Zzd84d713HjnuqN+QRZLaZAtnd0EQWPD6KNDHdOa+Ow7Luak+TMnqNLybO3s5jN3rmVfd3/Jdj9z5iKuPHX+iNsGBxNfe+AFHn6hs+RzLO5o5R1XrGTGOH6p3PL4Vn7w9I6SbWZNb+IdP7WS+W0tVb/OTXev43N3rx/1+wzQ2pjjD153OpefMq/q1ynlic1dfPm+DfQNjF5EU0PwpouWccZif28c725+dAt3PLuzZJs5M5p45xUnMWdGc01es9xQ5jll0hTQ3z/I7/7LT8YMZAD3r9vDh295ZhKqGt2tT24rGcgAtnb10NM/SHf/AP0lGnYe6uMdn72PgYGBCai0PPt7+vnnu8YOZADfeWwrD23YM+K2/3xs65iBDGBzZzc33b2eav/ovmfNrjEDGcDeg33ceNdauvuq69tbHt/KTWMEMoDu/kH+8ttP8vyO/VW9Timb9h4aM5AB9A0kvnzfBjbuOViynbLtR8/uHDOQAew+0MeNd66lp39yf27UNZRFRGNE/EVErI2IQxGxJiL+KCJK1hURV0bEAxHRXdjn3ZNVs3Q8+tajW9jS2TN2w4LvP7Wd3fvHDnAT5fP3lP5F3TcwcFQQ6BsYHL0xsHt/L//0o3U1qq5y963dTdehsQPZkFuf3H5MoNrf0889a3aV/Rwbdh/k6W37ym4/ZGAw8YOntpfdfveBPh5cP3KIHMvn711Pubmxu3+Qm+5eX9XrlHLb09vHDGRD+gYSt5URVpVN/QOD3PZ0+Z/tHft7eXjD3gms6Fj1Hin7APBu4DeA04H/Dfwu8Juj7RARK4GbgTuA84D/A3wsIq6b8Gql49S3HtlcUfu+gfxhsnp4ZONeNuw+VLLNngNHnz82MJgYHOO3+78+tGnctVVjcDBx79rdFe2z60Avz24/elTovnW7S44IjuSe58sPcUMe39xJVxkjeke9ToXvD+CB9XvYtKe7on3uW7uLfd19YzcsU+ehPp7YPOqRpBE9uaWLzkO1q0GT55FNnRzorWzkq9L/u+NV71B2GfDvKaVvp5TWpZT+BbgFuLDEPu8GNqSU3p9SejKl9P+AzwC/Mwn1Ssed7t5+1u6s/JBLtaMf41XOoYXuEQ4pDIwx2rF576G6HMLctq+7ql/iT289epTr2SpGvfIXSFQW5J7ZVvkhwh37eth9oLKR1R89V/mIU09/4sc1/CX5/I79Yx46HW4wwXPbK/9eqP6q+T+0pbO6/7/Vqnco+xHw0xFxKkBEnANcQX4kbDSXkQ9uxb4LXBgRx1wGFBEtEdE+tABttSldOj5UOuoxpLu/9CHBiXKgZ+x6R8oZ5fxu3VVhcKiF7r7q+nH41ZnVPM9ggt4xDu0e+7rVBddK9ztYxvd5JPur3G8k1Z4L11Pl91T1Ve3/xd5J/FlY73nKPgh0AE9FxADQAPxBSulLJfZZBGwbtm4b+fcyD9gybNv1wB/Xplzp+NPeWt1/89bG+vzNNr2MucUiOCaFlTM719waXUlVidam6vqxZVj/V/M8uYDmCudcqnb+sUr3m9Zc3eeyltMUVP1eq/yeqr6G/58qV/Mk/iys9yfrjcCbgV8BzgfeCvxORLx1jP2G/1Eco6wHuIF88BtallRdrXQcam1uZMXc6RXvd96y2RNQzdheumrsaQ9G+uHaUGJaDIDFHdNoaJj8yWQXtrXSPq3yIHHqwqMH9VctqHyQ/5QFM4mobDLZVQsqnzpk/sxmZk+vbL6yK6qY3qK5Mbh45ZyK9xvNKQtmUulcu7mAU+Z7wOV4tGph5d+3Re2tkzp5cL1D2V8B/zel9OWU0qMppc8Bf01+dGs0W8mPlhVbAPQDx5zVmlLqSSl1DS2AJwNoynntWcP/y5TWmAt+6cKlE1RNaecsnc3SOaUn6Zw9bMSrIRfkxggfP3/e4nHXVo1cLrh4RWVBYs6MJk5deHQ4unDFbBorTBCXnlT5XRrOPLGDtgpHVy85aW7F4e/CFXNYPKuy2fovWjGnJpPVDumY1sTpFU5Ke9qiNjoqDKDKhrOXdJQ1El/skpNq90dAOeodyqYDww/WDlC6rruBVw5b9yrg/pSSl8RII3j9OSeysL38CT6vWj2POTMn/1DfkF+5eBmlfsc3NzQcNWP9WLdFmT2jmXdcvrJW5VXskpPmVhR0XnHawmNCTltrU0W/IJbMnsZpiyofGWjIBVetHnny2pHMnt7EBcurG1X9lUtKf5+LtTQGb7m09nebuPLU+WWH3cZccNXqBTWvQZOjqSE36sTMI5k7o5nzls2awIqOVe9Q9k3gDyLidRGxIiKuBX4b+MZQg4i4ISJuKtrnU8DyiPhoRJweEe8A3gl8eFIrl44jjY05PviGs5lbRtA6f9ksPvAzp01CVaN71UsW8auXLi95aGlRewstjTlaGxtK/lJtn9bEP73lQprreB/MmS2NvO3yFcxsGbuGV56xYNSQ89ozT+CsEzvGfI5F7a289fIVFY9eDbn85HlceerYhxfbp+XfV7W3dHrNmSeMGcAhf9jy+teezilVHH4ay9I503njRUvHDGaNueCNFy1l6ZzKTwVQdrzs1PlcXsZ9fmdPb+JtP7ViQu7xWkpdb7MUEW3AnwPXkj8EuRn4EvBnKaXeQpsbgRUppauK9ruS/GHOlxT2+WBK6VNlvqa3WdKUtXt/L39/+3Pc9fyuY65Emt/WzGvOPIFfvXRZ3W+xNOS2p7fzpXs38PzOA8fc+/LMxR289bJlfP2hzdz65LZjZstvashx/vJZ/Pnrz2RRRzbuWbjnQC8/eHo7P3lhL73DpvBYPnc6L1s1f8zb+KSUuGfNbu5es4sd+46eEHhmSwMXLJ/DVavn1+Tel6PdH7ClMcd5y2Zx1eoFNTnf5vtPbefLP97AmhG+z+csmcXbf2oFZyweO4yOxwu7D3LbMzt4asux9748bVEbV61eYCB7EXlowx7ufG4nm/YePVdere/rOsR7X47CUCbBwd5+/uuJbWzf101jLscpC2by0lXlD+tPtme27eOeNbs41DtAW2sTL189nxOG3Rz6a/e/wKObOhkYHGTxrGm89dLlzJxWv0OwpRzqHeCprV0c6h2gsSHH0jnTOKGK4Lhmx3627+thMCU6pjWxemEbjRVebVmOjXsOsnlvN/0Dg8xoaWT1oraahL7hntrSxY/X7eZQ7wDt05p4xWkLWNhe2Xln49V5sI9nt++jp3+QlsYcqxZ4DtmL2Qu7D+bnMBxMzGzNf7YnYnTMUDYKQ5kkSZpM3pBckiTpOGIokyRJygBDmSRJUgYYyiRJkjLAUCZJkpQBhjJJkqQMMJRJkiRlgKFMkiQpAwxlkiRJGWAokyRJygBDmSRJUgYYyiRJkjLAUCZJkpQBhjJJkqQMMJRJkiRlgKFMkiQpAwxlkiRJGWAokyRJygBDmSRJUgYYyiRJkjLAUCZJkpQBhjJJkqQMMJRJkiRlgKFMkiQpAwxlkiRJGWAokyRJygBDmSRJUgYYyiRJkjLAUCZJkpQBhjJJkqQMqGsoi4h1EZFGWD4xSvu3jdK+dbJrlyRJqqXGOr/+RUBD0eMzgf8CvlZiny5gdfGKlFJ37UuTJEmaPHUNZSmlHcWPI+L3gOeB20vvlrZOaGGSJEmTLDPnlEVEM/Bm4DMppVSi6cyIWB8RGyPiWxFx3hjP2xIR7UML0FbLuiVJkmohM6EM+HlgFnBjiTZPAW8DrgF+GegG7oyIVSX2uR7oLFo21qBWSZKkmorSg1KTJyK+C/SmlH6ugn1ywIPAD1NK7xulTQvQUrSqDdjY2dlJe3v7eEqWJEkaU1dXFx0dHQAdKaWu0drV+0R/ACJiOXA18AuV7JdSGoyI+4BRR8pSSj1AT9FrVVumJEnShMnK4cu3A9uBb1eyU+QT1rnAlokoSpIkabLUfaSscAjy7cBnU0r9w7bdBGxKKV1fePzHwD3As0A78D7yoey9k1q0JElSjdU9lJE/bLkM+MwI25YBg0WPZwH/CCwif9L+Q8DLUko/nugiJUmSJlJmTvSfLIVpMTo90V+SJE2Gck/0z8o5ZZIkSVOaoUySJCkDDGWSJEkZYCiTJEnKAEOZJElSBhjKJEmSMsBQJkmSlAGGMkmSpAwwlEmSJGWAoUySJCkDDGWSJEkZYCiTJEnKAEOZJElSBhjKJEmSMsBQJkmSlAGGMkmSpAwwlEmSJGWAoUySJCkDDGWSJEkZYCiTJEnKAEOZJElSBhjKJEmSMsBQJkmSlAGGMkmSpAwwlEmSJGWAoUySJCkDDGWSJEkZYCiTJEnKAEOZJElSBhjKJEmSMsBQJkmSlAGGMkmSpAyoayiLiHURkUZYPlFin+si4omI6Cn8e+1k1ixJkjQR6j1SdhFwQtHyysL6r43UOCIuA74CfA44p/DvVyPikokvVZIkaeJESqneNRwWEX8D/CywKo1QWER8BWhPKb2maN13gD0ppV8u8zXagc7Ozk7a29trVLkkSdLIurq66OjoAOhIKXWN1q7eI2WHRUQz8GbgMyMFsoLLgFuGrfsucHmJ522JiPahBWirScGSJEk1lJlQBvw8MAu4sUSbRcC2Yeu2FdaP5nqgs2jZWH2JkiRJEyNLoeydwH+mlDaP0W74KFqMsK7YDUBH0bKk6golSZImSGO9CwCIiOXA1cAvjNF0K8eOii3g2NGzw1JKPUBP0WtVWaUkSdLEycpI2duB7cC3x2h3N0eu0BzyKuCuiShKkiRpstR9pCwicuRD2WdTSv3Dtt0EbEopXV9Y9bfADyPiA8C/A68nP8J2xSSWLEmSVHNZGCm7GlgGfGaEbcvIz18GQErpLuBN5EPcI8DbgDemlO6d+DIlSZImTqbmKZsMzlMmSZIm03E3T5kkSdJUZiiTJEnKAEOZJElSBhjKJEmSMsBQJkmSlAGGMkmSpAwwlEmSJGWAoUySJCkDDGWSJEkZYCiTJEnKAEOZJElSBhjKJEmSMsBQJkmSlAGGMkmSpAwwlEmSJGWAoUySJCkDDGWSJEkZYCiTJEnKAEOZJElSBhjKJEmSMsBQJkmSlAGGMkmSpAwwlEmSJGWAoUySJCkDDGWSJEkZYCiTJEnKAEOZJElSBhjKJEmSMsBQJkmSlAGGMkmSpAwwlEmSJGWAoUySJCkD6h7KIuLEiPh8ROyKiIMR8XBEXFCi/VURkUZYTpvMuiVJkmqpsZ4vHhGzgTuBHwCvAbYDJwN7y9h9NdBV9HhHzQuUJEmaJHUNZcAHgBdSSm8vWreuzH23p5TGDG8R0QK0FK1qK788SZKkyVHvw5fXAPdHxNciYntEPBQRv1bmvg9FxJaIuDUiXl6i3fVAZ9GycZw1S5Ik1Vy9Q9lJwHuAZ4FXA58CPhYRbymxzxbgXcB1wC8ATwO3RsTLRml/A9BRtCypTemSJEm1Eyml+r14RC9wf0rp8qJ1HwMuSildVsHzfBNIKaVrymjbDnR2dnbS3t5eTdmSJEll6+rqoqOjA6AjpdQ1Wrt6j5RtAZ4Ytu5JYFmFz3MPsKomFUmSJNVBvUPZneSvoix2KrC+wuc5j3zAkyRJOi7V++rLvwbuiojfB74KXEz+fLF3DTWIiBuAE1NKbyk8fj/5KzQfB5qBN5M/v+y6Sa1ckiSphuoaylJK90XEteRPxv8jYC3w/pTSF4qancDRhzObgQ8DJwKHyIez16WUbp6cqiVJkmqvrif614Mn+kuSpMl0vJzoL0mSJKoMZRHxMxFxRdHj9xbuWfnFwq2TJEmSVIFqR8r+CmgHiIizgI8AN5OfDPajtSlNkiRp6qj2RP+VHJlf7DrgWyml34+I88mHM0mSJFWg2pGyXmB64eurgVsKX++mMIImSZKk8lU7UnYn8NGIuJP83GJvLKw/FW/4LUmSVLFqR8reC/QBbwDek1LaVFj/GuA7tShMkiRpKql4pCwiGoGXA+9KKR11a6OU0m/VqjBJkqSppOKRspRSP/D35GfWlyRJUg1Ue/jyXvI3AZckSVINVHui/yeBj0TEEuAB4EDxxpTSI+MtTJIkaSqpNpR9pfDvx4rWJSAK/zaMpyhJkqSpZjyTx0qSJKlGqgplKaX1tS5EkiRpKqv2RH8i4lcj4s6I2BwRywvr3h8Rr69deZIkSVNDVaEsIt5D/sbjNwOzOHIO2V7g/bUpTZIkaeqodqTsN4FfSyn9JTBQtP5+4KxxVyVJkjTFVBvKVgIPjbC+B5hRfTmSJElTU7WhbC1w7gjrXwM8UX05kiRJU1O1U2L8FfCJiGglPzfZxRHxy8D1wH+vVXGSJElTRbVTYvxz4cbkHwKmA18ENgH/M6X05RrWJ0mSNCVUO1JGSunTwKcjYh6QSyltr11ZkiRJU0vVoWxISmlnLQqRJEmaysoOZRHxEPn7Wo4ppXR+1RVJkiRNQZWMlP1b0detwP8gf6Xl3YV1lwIvAT5Zm9IkSZKmjrJDWUrpT4e+joj/B3wspfT/FbeJiD8FltauPEmSpKmh2nnKfhG4aYT1nweuq74cSZKkqanaUHYIuGKE9VcA3dWXI0mSNDVVe/Xl3wB/HxEXAPcU1l0KvAP4s1oUJo1l3c4D3LNmF2t2HqC3f5CWphynL2rnkpPmcELHNPYf6uVTd6zlO49uYffBPlJKTGtu4OKVc3jfK1Zx0vyZVb/2pr0H+cqPX+DuNbvY391PLhcs7mjltWct5ufOPoHGxmr/3tFwa4e+zzv20zeQaGnKccYJ7Vx60lwWtrfWuzxJqplIqawLKo/dMeKXgP8JnF5Y9STwtymlr9aotgkREe1AZ2dnJ+3t7fUuR1U42NvPF+7ZwJqdB0ZtEyRueWIrvf0jf74jgp89exF/ee3ZFb/+x259lm/+ZDODo/zX6ZjWyJ9c8xLOXjKr4ufWEQd6+vnCvetZu/PgqG3OWzqLXzj/RBobDMGSsqurq4uOjg6AjpRS12jtqg5lxytD2fGtu2+AT/9wDZs7Rz9KvnH3Qe5dt5sc0NQQRMSobV931gnccF35weyjtzzNtx/dOma71sYcf/WLZ3PG4o6yn1tHdPcN8A+3r2Fr19hnQ5x+QhtvvmQ5udzo32dJqqdyQ9m4/ryMiOaIWBIRy4qXCp/jxIj4fETsioiDEfFw4bBoqX2ujIgHIqI7ItZExLvH8z50/Pj+U9tLBjKABzfsIaXEQEoMjPE3x7cf3cL9a3eV9do/eWFPWYEMoLt/kA9+5+my2upY//XEtrICGcCTW/bxwIY9E1yRJE28qkJZRKyKiDvIn/C/HlhbWNYV/i33eWYDdwJ9wGuAM4D/Bewtsc9K4GbgDuA84P8AH4sIr/p8kesbGOSB9aV/+T6/fT+9A4OHHw+MdoyxyKd+uKas1//q/RvLajdk455DY9arY/X0D/BghSHrnufLC9aSlGXVnuh/I9AP/CywhTJn+h/BB4AXUkpvL1q3box93g1sSCm9v/D4yYi4EPgd4OtV1qHjwBObuzjYO1CyzZqd+496PJgSg4Op5KGthzbsZWBggIaGhlHbdPf282AVAevfH97EBctnV7zfVPb45i66+wbHblhkc2c3m/Ye4sRZ0yaoKkmaeNWGsnOBC1JKT43z9a8BvhsRXwOuBDYBnyzc7Hw0lwG3DFv3XeCdEdGUUuor3hARLUBL0aq2cdasOtl9sHfMNj39x/4yH+svhr6BQXbs72VRx+i/0Hfs66V3rGOhI+7XU/E+U92eA2N/n0fbz1Am6XhW7TllTwDzavD6JwHvAZ4FXg18ivyhyLeU2GcRsG3Yum3kA+ZINV0PdBYtlR2D0nGl2lO9PUdcklRv1YayDwAfioirImJuRLQXLxW+/oMppd9PKT2UUvoH4NPkg1opw4csYpT1ADcAHUXLkgrqU4bMm9EyZpuWpmMPQZa4+BKA5sYcc2c0l2wzv62Z5sbKk5vzaFVu7syxv88j71f6eyhJWVdtKPse+clibwW2A3sKy97Cv+XaQn7UrdiTQKkrOLeSHy0rtoD8OW7HnO2bUupJKXUNLcC+CupThpx+QhszW0Y/7wvglPkzjnqciyA3Riq7cPmckueTAbQ2N3LxyrnlFVrkDRf4N0ClXrK4nenNpb8fwy2ZPY0TShx+lqTjQbXnlL28Rq9/J7B62LpTyV/ROZq7gZ8btu5VwP3DzyfTi0tjQ44LV8zhtqd3jNpmxbyZPLqp8/C5ZQ1jHJeMgPe+/OSyXv+NFy7hzud2Uu7UfsvnTuPME52nrFJNDTkuXD6bHz67s+x9Lju58sAsSVlT1UhZSun2UksFT/XXwKUR8fsRcUpE/ArwLuATQw0i4oaIKL75+aeA5RHx0Yg4PSLeAbwT+HA170XHl1ectoBlc6aXbHPRijnkImiIoGGMI45vuGAJZ5U58/4Zizt4w/nljXzNaGngD153RlltdayfPn0hS2aXN/J1zpIOzlvq3RMkHf/KntE/Is4GHkspDRa+HlVK6ZGyC4j4WfLnfa0iP8fZR4uvvoyIG4EVKaWritZdST7QvQTYDHwwpfSpMl/PGf2Pc919A3zt/hd4YsvIR6IjYGZLA//x8OZRp9BoyAVvvHApv/fa00fcXso/3bGGrz2wkb5Rrsac39bMn73+TE5d6IW+49HdN8BX7nuBp7aO/n2+ZOUcfu7sxc7mLynTan6bpYgYBBallLYXvk6MfLFbSilVdkLIJDKUvXhs7ezmnjW7eH7Hfnr7B2ltauD0E9q4eOVc5sxoZmBggH++az3feGgjO/f3MpgSM5obeemqefzmK05hQXv15yDt3t/L1x54gR89t5Ou7j4ac8GJs6ZzzTkn8IrTFpDLeS/GWtnSeahwQ/IDRd/ndi5ZOYfZY1ygIUlZMBGhbDn5SVtT4etRpZRKnRNWV4YySZI0mcoNZWWf6F8ctLIcuiRJko5HZYeyiLim3LYppf+orhxJkqSpqZIpMf6tzHYJyOw5ZZIkSVlUyeFLz1yWJEmaIFUFrYhYWetCJEmSprJqR7+ei4gfRMSbI8Kb+0mSJI1TtaHsHOAh4CPA1oj4h4i4uHZlSZIkTS3V3mbpsZTSbwMnAm8nf4PwH0XE4xHx2xExv5ZFSpIkvdiN6+T9lFJ/SukbwC8BHwBOJn8Pyo0RcVNEnFCDGiVJkl70xhXKIuLCiPgksAX4bfKB7GTgFeRH0f593BVKkiRNAZXMU3ZYRPw2+cOWq4GbgbcAN6eUBgtN1kbErwNP1aRKSZKkF7mqQhnwHuAzwD+nlLaO0mYD8M4qn1+SJGlKqSqUpZRWldGmF/hsNc8vSZI01VR0TllErIqIL0VE+wjbOiLiixFxUu3KkyRJmhoqPdH/d4EXUkpdwzeklDqBFwptJEmSVIFKQ9nLgK+V2P5V8ldeSpIkqQKVhrLlwPYS23cCS6svR5IkaWqqNJR1kp+HbDSnAMcc2pQkSVJplYayHwK/WWL7+4A7qi9HkiRpaqp0SowbgLsj4l+ADwFPF9afBvxv4NXA5bUrT5IkaWqoKJSllB6KiDeQnzj22mGbdwG/lFJ6sFbFSZIkTRUVTx6bUvpWRCwnPyq2CgjgGeCWlNLBGtcnSZI0JVQ7o/+hiLga+KOU0u4a1yRJkjTlVDqj/5Kih78CzCysfzQinApDkiSpSpWOlD0VEbuAO4FW8nOSbQBWAE21LU2SJGnqqHRKjA7gF4EHCvveHBHPAC3AqyNiUY3rkyRJmhIqDWVNKaUfp5Q+AhwCzgPeDgwA7wCej4inSz2BJEmSjlXp4cuuiHiI/OHLZmB6SunOiOgH3ghsBC6ucY2SJEkvepWOlC0G/gLoIR/o7o+IO8gHtPOBlFL6UW1LlCRJevGrKJSllHamlPR8Q3UAABznSURBVL6ZUroeOAhcBHwcSMCHyY+k3V77MiVJkl7cKh0pG64zpfRVoA94BbAS+OS4q5IkSZpixhPKziZ/DhnAeqAvpbQ1pfSVcp8gIv4kItKwZWuJ9leN0D5FxGnjeB+SJEl1V9WM/gAppReKvj5zHDU8Dlxd9HigjH1WA11Fj3eM4/UlSZLqrupQVkP9KaVRR8dGsT2ltHdCqpEkSaqD8Z5TVgurImJzRKyNiC9HxEll7PNQRGyJiFsj4uWlGkZES0S0Dy1AW23KliRJqp16h7J7gbcArwZ+DVgE3BURc0dpvwV4F3Ad8AvA08CtEfGyEq9xPdBZtGws0VaSJKkuIqVU7xoOi4gZwPPAh1JKHy1zn2+Snx/tmlG2t5C/DdSQNmBjZ2cn7e3t4y1ZkiSppK6uLjo6OgA6Ukpdo7Wr90jZUVJKB4BHgVUV7HZPqfYppZ6UUtfQAuwbZ5mSJEk1l6lQVhjVOp38YcpynVdhe0mSpMyp69WXEfFh4JvABmAB8IdAO/DZwvYbgBNTSm8pPH4/sI78NBrNwJvJn1923WTXLkmSVEv1nhJjCfAlYB75ucbuAS5NKa0vbD8BWFbUvpn87ZxOBA6RD2evSyndPGkVS5IkTYBMneg/GQrTYnR6or8kSZoMx+WJ/pIkSVOVoUySJCkDDGWSJEkZYCiTJEnKAEOZJElSBhjKJEmSMsBQJkmSlAGGMkmSpAwwlEmSJGWAoUySJCkDDGWSJEkZYCiTJEnKAEOZJElSBhjKJEmSMsBQJkmSlAGGMkmSpAwwlEmSJGWAoUySJCkDDGWSJEkZYCiTJEnKAEOZJElSBhjKJEmSMsBQJkmSlAGGMkmSpAwwlEmSJGWAoUySJCkDDGWSJEkZYCiTJEnKAEOZJElSBhjKJEmSMsBQJkmSlAF1DWUR8ScRkYYtW8fY58qIeCAiuiNiTUS8e7LqlSRJmiiN9S4AeBy4uujxwGgNI2IlcDPwaeDNwE8Bn4yIHSmlr09olZIkSRMoC6GsP6VUcnSsyLuBDSml9xcePxkRFwK/AxjKJEnScSsL55StiojNEbE2Ir4cESeVaHsZcMuwdd8FLoyIppF2iIiWiGgfWoC2GtUtSZJUM/UOZfcCbwFeDfwasAi4KyLmjtJ+EbBt2Lpt5Ef85o2yz/VAZ9GycZw1S5Ik1VxdQ1lK6T9TSl9PKT2aUvoe8LrCpreW2m3Y4xhl/ZAbgI6iZUm19UqSJE2ULJxTdlhK6UBEPAqsGqXJVvKjZcUWAP3ArlGeswfoGXocESM1kyRJqqt6H748SkS0AKcDW0ZpcjfwymHrXgXcn1Lqm8jaJEmSJlK95yn7cGHesZURcQnwL0A78NnC9hsi4qaiXT4FLI+Ij0bE6RHxDuCdwIcnvXhJkqQaqvfhyyXAl8ifpL8DuAe4NKW0vrD9BGDZUOOU0tqIeC3w18B7gc3A+5yjTJIkHe8ipdHOj39xKkyL0dnZ2Ul7e3u9y5EkSS9yXV1ddHR0AHSklLpGa5epc8okSZKmKkOZJElSBhjKJEmSMsBQJkmSlAGGMkmSpAwwlEmSJGWAoUySJCkDDGWSJEkZYCiTJEnKAEOZJElSBhjKJEmSMsBQJkmSlAGGMkmSpAwwlEmSJGWAoUySJCkDDGWSJEkZYCiTJEnKAEOZJElSBhjKJEmSMsBQJkmSlAGGMkmSpAwwlEmSJGWAoUySJCkDDGWSJEkZYCiTJEnKAEOZJElSBhjKJEmSMsBQJkmSlAGGMkmSpAwwlEmSJGWAoUySJCkDDGWSJEkZkJlQFhHXR0SKiL8p0eZthTbDl9bJrFWSJKnWGutdAEBEXAS8C3ikjOZdwOriFSml7omoS5IkabLUfaQsImYCXwB+DdhTxi4ppbS1eJnYCiVJkiZe3UMZ8Ang2yml75XZfmZErI+IjRHxrYg4r1TjiGiJiPahBWgbd8WSJEk1VtdQFhFvAi4Ari9zl6eAtwHXAL8MdAN3RsSqEvtcD3QWLRurrVeSJGmiREqpPi8csRS4H3hVSuknhXW3AQ+nlN5f5nPkgAeBH6aU3jdKmxagpWhVG7Cxs7OT9vb2cbwDSZKksXV1ddHR0QHQkVLqGq1dPU/0vwBYADwQEUPrGoCXRcRvAC0ppYFST5BSGoyI+4BRR8pSSj1Az9DjoteSJEnKjHqGsluBs4at+2fyhyg/OFYgA4h8wjoXeLT25UmSJE2euoWylNI+4LHidRFxANiVUnqs8PgmYFNK6frC4z8G7gGeBdqB95EPZe+dxNIlSZJqLhPzlJWwDBgsejwL+EdgEfmT9h8CXpZS+nEdapMkSaqZup3oXy+FaTE6PdFfkiRNhnJP9M/CPGWSJElTnqFMkiQpAwxlkiRJGWAokyRJygBDmSRJUgYYyiRJkjLAUCZJkpQBhjJJkqQMMJRJkiRlgKFMkiQpAwxlkiRJGWAokyRJygBDmSRJUgYYyiRJkjLAUCZJkpQBhjJJkqQMMJRJkiRlgKFMkiQpAwxlkiRJGWAokyRJygBDmSRJUgYYyiRJkjLAUCZJkpQBhjJJkqQMMJRJkiRlgKFMkiQpAwxlkiRJGWAokyRJyoDGehfwYjIwmHhySxc79vdAglnTmzhjcTstjQ0VPc/2fd08s3U/Pf0DtDQ2cOrCmUxvaeTxTZ08vrmLp7Z20dKYY8ns6Vx56nxOO6F9gt7R+PQPDPLU1n2H+yOAyEH/QKIxlyORSEONE0Tk+7ClsYFTF81kQVvruF5/095DrNmxn97+QaY1N3D6onZmz2gG4IXdB1m368DhbWec0M6s6c3jej1JksYjUkpjt3oRiYh2oLOzs5P29tqEmf6BQW5/Zgc/Xrubru7+o7a1NuU4f9lsrj59IdOaS4ez53fs5/tPbmfNzgOH13X3DbBpzyF27e+hq6efnr6Bw9sacsH0lkbOWNTGWy5fwUtXza/J+xmvvoFBfvDUdu5bt5v9PQPs6+5j095DdB3qJxf5ugdSYnAQmhqCAHoHEo0NwYKZLSye1Uoul+Pk+TN4+WkLOHn+zIpe/4nNXfzg6e1s3HPoqPUR0NbSSAL2Dfs+5QJWL2rj6tMXsnjWtHH2gCRJR3R1ddHR0QHQkVLqGq2doWyc+gYG+exd63h+x4GS7Ra0tfDfX7qSttamEbc/uGEPX39gI4NF344DPf08vXUfuw700HmoD4CmhhyNuThq39bmBmZNa+JdLz2JN1y4dHxvaJx6+gf45zvXsX7XQQB27+/h+Z0HSAlSSuw91Ef/wCANuRytTTkO9OTDUVtrI61N+YHbGS0NnLaojYZcjlzAdRcs4fxls8t6/Tue3cHNj24dcdvmvYfYuOcQuYBTFswccWSspTHHmy9dxikL2qp5+5IkHaPcUOY5ZeP0jQc3jRnIALbv6+Gmu9czUghet/PAMYGsb2CQZ7bto6u773AgG1o/OOwpunsH2N/dzz/esYYfr91V9Xupha/dv/FwINvf3X84kAF0decDGUBv/yC7D/Qe3m9fdz99hW0HegZ4bvt+AAYTfP2BjazfNXYfP7apc9RAtnt/z+GRs8EEz23fz6HegWPa9fQP8vl7NrBzf0+Z71iSpNrITCiLiOsjIkXE34zR7rqIeCIiegr/XjtZNQ63+0AvD2/cW3b7jXsO8WwhbBS7/ZkdxwStHft66BtIRwWyIUPBptjB3gH6BxOfv2dD2fXU2raubh7ffOQPgC1dhw4Hsv6BQXr7j9Q9MDjIYEoMFL3xg71HDil2Huo/PIo2mPJ9NJbbnt4+6rZNnUcfyhxMsLXr0Ihte/oHufO5nWO+niRJtZSJUBYRFwHvAh4Zo91lwFeAzwHnFP79akRcMuFFjuDeNbuo9OjvPWuOHsnac6CXp7ftO2pdSont+3ro7R84PHpUbCAlhq8dTInevkGe3NLFC3sOVlZUjRS/t97+QfYePBIoDxWdCzeY8u8BOCqU9fYPMjB45J1t6+o+/PVTW/exp2hkbbgNuw6yaW/3iNv2dfdxqPfYfty1v3fEgAvw0Ia99PQfO5ImSdJEqXsoi4iZwBeAXwP2jNH8/cB/pZRuSCk9lVK6Abi1sH6052+JiPahBajZyULP7zh21GvMfYaNlK3Zuf+YYNfdnx9VOtg3eigYHD60BvQWDm3e/Xx9DmEWv7d93X1Hva/eovAzWLRhcNibL25XfNFEShx1AcQxr71z9O9F1wijjfnX5vBo3HA9/YPHXCggSdJEqnsoAz4BfDul9L0y2l4G3DJs3XeBy0vscz3QWbRsrKbIkRQfjit7n4F01HllPSM8x1DgSiMEr1KGnnakc6UmQ+/AkXoHhtU+2ojiMauLVgwPnqX6u9S2gRLdWGpbNd9fSZKqVddQFhFvAi4gH5zKsQjYNmzdtsL60dwAdBQtSyosc1QtTZXNPwb5q/sijlw92TrCczQUrq7MDbvKcixDTzuzpfK6aqG16cjHafgVoqO9leGri7rmcD+M9PzHvvbo77mxxKd8+GuU+5ySJNVa3UJZRCwF/hb4bymlkU8GGtnwsY0YYd2Rxin1pJS6hhZg32htK3X6CZUfCT1j2ESvpy5sO3aKi6YGpjXlmN48+ty+I4WJ5sb8dBlXrq7PfGWnLTrSH+3Tm44KYs1FyaihKHkND57NRRPtzpp+ZPqQxlywauHo/X36otG3jTYpbGMuaGsZuY9ntjSwdLbzlUmSJk89R8ouABYAD0REf0T0A1cC7ys8HmmYYivHjoot4NjRs0lx0Yo5NFTYg5ecNOeoxzNbGnnJ4mPnS1vQ3kpTQ+6oMDOkIeKYEaZcLmhpzHHuslnMmzm+mfCrdcnKuYdHuhpzOebMOBKGphWNOkUcCWbFgbSlMUeuKLAtbGs5/PVZJ3Ywc5QABfn+OmnejBG3TW9uHHHfeW0to45GXrhiDo2VfnMlSRqHev7WuRU4Czi3aLmf/En/56aURjox6m7glcPWvQq4awLrHFVbaxOXnzyv7PanLWpj+dxjg8PLT1tAy7DwNW9mC61NOWYNm2w2YMSwMKO5kebGHG+/fEXZ9dTa7BnNXLLySOhcPKv1cGjNTxZ7JJg1NuRozB0JYQFMLwpO82Y201oYKWxpzJU1+nf1GQtHDclLZrcedWi0qSFY1D5yeG1vbeSyk+eO+XqSJNVS3UJZSmlfSumx4gU4AOwqfE1E3BQRNxTt9rfAqyLiAxFxWkR8ALgaKDm32UR6zZmLOH/ZrDHbnTRvBm+6eOTZ9he2t/LmS5cfFcwacsHqhW3MmtF8eMQpyB8GHD64M6OlkY5pjfzez5xW9/tg/tzZizl7SQcArU2NnLqw7XBQmtnaeHjkr6Uxx9wZzUQEEfnDnY25/LbZ05tYWRj1ys+wv5yFowSoYivnzeCXLlx6zOFggPZpzZw0bwYR+UB26sK2EUch21obedtPraB9lDsvSJI0UTJ1m6WIuA14OKX0/qLH61JKbytq8wbgL4CTgOeBP0gp/WsFr1Hze18CPLRhD3c9v+uYaRTmz2zmkpPmcsnKsQ+Hbd/XzR3P7OSRjXsPX8nYPzDIjv097DvUz879Pew91Hf46s3mxhztrU1cdvJcfvXS5XUPZENSSjy4YQ93P7+LTXu76e4bYGvnIXYd6KWpIUdLY47e/kF6+gdpa20kyE9/0drUwIK2Fha0tdDcmOPsJbN46anzKr4x+cY9B/nRszt5bHMnxdOQtTTmWD53OgMDiXW7Dxy1bVpTA+cvn8VLT5lPx3QDmSSpdrz35SgmKpQN2bz3EDv395BS/kT1ZXOmH3W1ZTkO9Q6wducBevoHaGlsYOW8GTQ35lizYz8b9xzkiS1dTGtqYEFbK1esmjfqiexZsHHPQXYf6CUlmN7cQN9Aoqd/gObGHM0NOQ4Wpu8o3jb0nse6gftY9nX3sX7XQfoGBmltauCk+TNoKVxI0NXdx4bCtunNjYf7WJKkWjOUjWKiQ5kkSVIxb0guSZJ0HDGUSZIkZYChTJIkKQMMZZIkSRlgKJMkScoAQ5kkSVIGGMokSZIywFAmSZKUAYYySZKkDGisdwH10tU16oS6kiRJNVNu5piKt1k6EdhY7zokSdKUsySltGm0jVMxlAWwGNhX46duIx/2lkzAc0919u3EsW8njn07cezbiWPfTpw2YHMqEbym3OHLQmeMmlKrlc96AOwrdbNRVc6+nTj27cSxbyeOfTtx7NsJNWZ/eqK/JElSBhjKJEmSMsBQVjs9wJ8W/lVt2bcTx76dOPbtxLFvJ459W0dT7kR/SZKkLHKkTJIkKQMMZZIkSRlgKJMkScoAQ5kkSVIGGMoqEBF/EhFp2LK1aHsU2myOiEMRcVtEvKSeNWdVRLwsIr5Z6KsUET8/bPuYfRkRsyPicxHRWVg+FxGzJvedZE8ZfXvjCJ/je4a1aYmIj0fEzog4EBH/ERFLJvedZE9EXB8R90XEvojYHhH/FhGrh7UZs+8iYlnhe3Sg0O5jEdE8ue8mW8rs29tG+Ox+eVgbfy4MExHviYhHIqKrsNwdEa8p2u5nNiMMZZV7HDihaDmraNv/Bn4b+A3gImAr8F8R0TbZRR4HZgA/Id9XIymnL78InAv8TGE5F/jcRBV8HBmrbwG+w9Gf49cO2/43wLXAm4ArgJnAtyKioebVHl+uBD4BXAq8kvxdUW6JiBlFbUr2XeHfb5P/Pl1RaHcd8JFJeg9ZVU7fAnyaoz+7vz5suz8XjrUR+D3gwsLyfeDfi/7Q9TObFSkllzIX4E+Ah0fZFsAW4ANF61qAvcCv17v2LC9AAn6+kr4ETi/sd0lRm0sL61bX+z1lZRnet4V1NwL/VmKfDqAXeGPRusXAAPDqer+nLC3A/EIfv6zcvgNeU3i8uKjNm4BuoL3e7ykry/C+Lay7DfibEvv4c6H8/t0NvNPPbLYWR8oqt6pwWGhtRHw5Ik4qrF8JLAJuGWqYUuoBbgcur0Odx7Ny+vIyoDOldG9Rm3uATuzvclxVOET0TER8OiIWFG27AGji6P7fDDyGfTtcR+Hf3YV/y+m7y4DHCuuHfJf8Hx4XTGi1x5fhfTvkvxUOnz0eER8eNnruz4UxRERDRLyJ/KjX3fiZzZQpd0PycboXeAvwDLAQ+EPgrsIQ8KJCm23D9tkGLJ+0Cl8cyunLRcD2EfbdXrS/RvafwNeA9eQD8J8D34+ICwrhdxHQm1LaM2y/bdi3h0VEAB8FfpRSeqywupy+W8Swz3ZKaU9E9GL/AqP2LcAXgLXkT2c4E7gBOIf84U7w58KoIuIs8iGsFdgPXJtSeiIizsXPbGYYyiqQUvrPooePRsTdwPPAW4GhE6WH3yIhRlin8ozVlyP1q/09hpTSV4oePhYR95MPaK8D/rXErvbt0f4OOJv8OTZj8bNbmRH7NqX06aKHj0XEs8D9EXF+SunBoWYjPJ99C0+TP79uFvnzwT4bEVeWaO9ntg48fDkOKaUDwKPAKvJ/ucGxfzUs4NgRH5VWTl9uJT9aOdx87O+KpJS2kA9lqwqrtgLNETF7WFM/ywUR8XHgGuDlKaWNRZvK6butDPtsF9o3Yf+W6tuRPAj0cfRn158LI0gp9aaUnksp3Z9Sup78xUD/Ez+zmWIoG4eIaCF/YukWjgypv7JoezP5K4ruqkuBx69y+vJuoCMiLi5qcwn581Ds7wpExFxgKfnPMcAD5H/RFff/CeQPF03pvo28vwN+AXhFSmntsCbl9N3dwJmF9UNeRf4G0A9MVO1ZV0bfjuQl5IPB0GfXnwvlC/LnhPmZzZJ6X2lwPC3Ah8kHg5XAJcA3gS5geWH7B8hfIXgt+Q/0F4HNQFu9a8/aQv6S63MLSwJ+q/D1snL7kvy5UT8hf3XVpcAjwDfr/d7qvZTq28K2D5M/cXcFcBX5H7wbh/Xt3wMvAD8NnAfcCjwMNNT7/dW5bz9Z+FxeSX7kYGiZVm7fAQ3kR9i/V9j+04X2H6/3+8ty3wInA39EfkqHFeSncXmS/GhZQ9Hz+HPh2L79P8BLC/12FvCX5K+mfGVhu5/ZjCx1L+B4WoAvF4JBL7AJ+DpwRtH2ID9txhbylwrfDpxZ77qzuBTCQBphubHcvgTmAJ8nH4y7Cl/Pqvd7q/dSqm+BaeSvmtpe+ByvL6xfOuw5WoGPA7uAg+T/AFlaj/eTpWWUfk3A2yrpO/IB+VuF7bsK7Vvq/f6y3LfkR3NvL/RXD/Ac8LfAnGHP48+FY/v2n4B1hX7bXghXryza7mc2I0sUOluSJEl15DllkiRJGWAokyRJygBDmSRJUgYYyiRJkjLAUCZJkpQBhjJJkqQMMJRJkiRlgKFMkiQpAwxlkiRJGWAok1R3EXFjRPzbCOuviogUEbPqUZckTSZDmaQXtYhorncN9TKV37t0PDKUSTquRMR1EfF4RPRExLqI+F/Dtq+LiD8sjL51Ap+OiOaI+LuI2BIR3YU21xft0xER/xgR2yOiKyK+HxHnlKhhRWEE700RcVfhOR+PiKuGtbsyIn5cqHVLRPzfiGgsbPu5iNgbEbnC43MLz/lXRfv/Q0R8qejx5RHxw4g4FBEvRMTHImJGqfdedUdLmnSGMknHjYi4APgq8GXgLOBPgD+PiLcNa/q7wGPABcCfA+8DrgF+CVgNvBlYV3jOAL4NLAJeW9jnQeDWiJgzRkl/BXwEOA+4C/iPiJhbeN4TgZuB+4BzgPcA7wT+sLDvD4G2wr4AVwI7C/8OuQq4vfB8ZwHfBf4VOBt4I3AF8HdjvHdJx4lIKdW7BklTXETcSD4odQ/b1AC0ArNTSnsj4gvA/JTSq4r2/RDwupTSSwqP1wEPpZSuLWrzMeAlwNVp2A+9iHgF8A1gQUqpp2j9c8CHUkr/OEK9K4C1wO+llD5YWNdYWPfxlNKHIuIvgeuA04deMyL+B/BBoCOlNBgRDwBfTCl9JCK+QT7A/TEwD5gBbCns/1RE3AQcSin9elEdV5APbTNSSt0jvXdJxw9HyiRlxQ+Ac4ct/31Ym9OBO4etuxNYFRENRevuH9bmxsLzPV045Peqom0XADOBXRGxf2gBVgInj1Hz3UNfpJT6C697elGtdw8LgXcWXmtJ4fFtwFWF0bqXAv9OfpTrCuDlwLaU0lNFdb5tWI3fJf9zfGWJ9y7pONFY7wIkqeBASum54hURsWRYmwCGD+/HSM9V/CCl9GBErAReA1wNfDUivpdSegP5ULOF/KHC4faWX/6Rlyuj1qH1t5E/pHkOMAg8QX7k60pgduHrITngH4CPjfCaG4q+PjDCdknHAUOZpOPJE+RHkYpdDjyTUhootWNKqQv4CvCViPgX4DuFc8YeJH8+WX9KaV2F9VxK/tywocOXF3DkHK8ngOsiIopGyy4H9gGbCo+Hzit7P3B7SilFxO3A9eRD2d8WvdaDwEuGB1dJLx4evpR0PPkI8NMR8f9FxKkR8VbgN4APl9opIn6rcKXkaRFxKvCLwFbyI2HfI38Y8t8i4tWFKysvj4i/iIgLx6jnvRFxbUScBnyCfJD6TGHbJ4GlwMcLr/t64E+Bj6aUBgFSSp3Aw+TPp7utsN8PgfOBU4vWQf5ctMsi4hOFKzVXRcQ1EfHxMWqUdJwwlEk6bqSUHiR/BeWbyJ979WfAH6WUbhxj1/3AB8ifb3UfsAJ4bUppsDCK9VryYegzwDPkr+5cAWwb43l/r/C8PyF/TtjrU0o7C7VuKjzvxYXtnwL+CfiLYc/xA/IXNNxW2G8P+VG2HcCTRe/9EfKHNVcBdwAPkb+6cssYNUo6Tnj1pSRVqOjqy/NSSg/XtxpJLxaOlEmSJGWAoUySJCkD/v/27JgGAACAQZh/19jgaFWQzX0JADBgKQMAGBBlAAADogwAYECUAQAMiDIAgAFRBgAwIMoAAAZEGQDAQM8qwhq6F1PEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#horse = np.array([float(dd[4]) for dd in data[1:]])\n",
    "#cylinder = np.array([float(dd[2]) for dd in data[1:]])\n",
    "horse = data['Horse power']\n",
    "cylinder = data['cylinder number']\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(7, 5), dpi=100)\n",
    "\n",
    "#s: marker size; color: marker color; alpha: marker opacity.\n",
    "#e.g. ax.scatter(x, y, s=10)\n",
    "#https://problemsolvingwithpython.com/06-Plotting-with-Matplotlib/06.10-Scatter-Plots/\n",
    "ax.scatter(horse, cylinder, alpha=0.6, edgecolor='none', s=100)\n",
    "ax.set_xlabel('Horse power')\n",
    "ax.set_ylabel('#Cylinders')\n",
    "\n",
    "print (scipy.stats.spearmanr(horse, cylinder))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 2**. \n",
    "Compute the spearman rank correlation between \"Horse power\" and \"Engine displacement\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SpearmanrResult(correlation=0.8510426269929073, pvalue=6.791337587146898e-10)\n",
      "[[1.         0.79094859]\n",
      " [0.79094859 1.        ]]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "horse = data['Horse power']\n",
    "engine = data['Engine displacement']\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(7, 5), dpi=100)\n",
    "ax.scatter(horse, engine, alpha=0.6, edgecolor='none', s=100)\n",
    "ax.set_xlabel('Horse power')\n",
    "ax.set_ylabel('Engine displacement')\n",
    "\n",
    "print (scipy.stats.spearmanr(horse, engine))\n",
    "\n",
    "#print(np.corrcoef(horse, engine))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## <span style=\"color:#0b486b\">2. Linear Regression</span>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we investigate a simple case by fitting a linear regression for three data points. First we simulate the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x: [[0. ]\n",
      " [1. ]\n",
      " [2. ]\n",
      " [1.5]]\n",
      "y: [1, 1.5, 3.1, 1.5]\n"
     ]
    }
   ],
   "source": [
    "# simulating the data\n",
    "\n",
    "#numpy.c_ Translates slice objects to concatenation along the second axis. This is short-hand for np.\n",
    "#np.c_[np.array([[1,2,3]]), 0, 0, np.array([[4,5,6]])]\n",
    "#output: array([[1, 2, 3, 0, 0, 4, 5, 6]])\n",
    "#https://stackoverflow.com/questions/10894323/what-does-the-c-underscore-expression-c-do-exactly\n",
    "x = np.c_[0, 1, 2, 1.5].T\n",
    "y  = [1, 1.5, 3.1, 1.5]\n",
    "\n",
    "print (\"x:\",x)\n",
    "print (\"y:\",y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'y')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plotting the data\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(5, 5), dpi=100)\n",
    "ax.scatter(x, y, c='r')\n",
    "ax.set_title('simulated data')\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we fit the linear regression:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "\n",
    "# instanciate the model\n",
    "lr = linear_model.LinearRegression()\n",
    "\n",
    "# fit the model\n",
    "lr.fit(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: [0.89714286]\n",
      "   Intercept: 0.7657142857142858\n"
     ]
    }
   ],
   "source": [
    "print (\"Coefficients:\", lr.coef_)\n",
    "print (\"   Intercept:\", lr.intercept_)\n",
    "# print (\"    Residues:\", lr.residues_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the line to see how it estimates our data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'y')"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "yhat = lr.predict(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(5, 5), dpi=100)\n",
    "ax.scatter(x, y, c='r')\n",
    "ax.plot(x, yhat)\n",
    "\n",
    "ax.set_title('simulated data and the estimated line')\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the method `predict()` to predict `y` for a new `x`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_test.T: [[4.  2.3]]\n",
      "y_test: [4.35428571 2.82914286]\n"
     ]
    }
   ],
   "source": [
    "x_test = np.c_[4, 2.3].T\n",
    "y_test = lr.predict(x_test)\n",
    "\n",
    "print (\"x_test.T:\", x_test.T)\n",
    "print (\"y_test:\", y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id = \"mlr\"></a>\n",
    "\n",
    "\n",
    "### <span style=\"color:#0b486b\">2.1 Multiple Linear Regression</span>\n",
    "\n",
    "\n",
    "Multiple linear regression attempts to model the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed data. Every value of the independent variable x is associated with a value of the dependent variable y. For example if we have two explanatory variables (attributes, features), our data has such a form:\n",
    "\n",
    "$$\n",
    "D=\\left\\{ \\left(\\left(x_{1,1},x_{2,1}\\right),y_{1}\\right),\\left(\\left(x_{1,2},x_{2,2}\\right),y_{2}\\right),\\ldots,\\left(\\left(x_{1,n},x_{2,n}\\right),y_{n}\\right)\\right\\} \n",
    "$$\n",
    "\n",
    "Now we fit a multiple linear regression $y = x_1 + 2x_2 + 1$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0]\n",
      " [0 1]\n",
      " [1 1]\n",
      " [1 0]]\n",
      "[1.5, 3.2, 4, 2]\n"
     ]
    }
   ],
   "source": [
    "# simulate the data\n",
    "\n",
    "x = np.c_[[0, 0], [0, 1], [1, 1], [1, 0]].T\n",
    "y = [1.5, 3.2, 4, 2]\n",
    "\n",
    "print (x)\n",
    "print (y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mlr = linear_model.LinearRegression(fit_intercept=True)\n",
    "mlr.fit(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mlr.coef_: [0.65 1.85]\n",
      "mlr.intercept_: 1.425\n"
     ]
    }
   ],
   "source": [
    "print (\"mlr.coef_:\", mlr.coef_)\n",
    "print (\"mlr.intercept_:\", mlr.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mlr.predict(x): [1.425 3.275 3.925 2.075]\n"
     ]
    }
   ],
   "source": [
    "print (\"mlr.predict(x):\", mlr.predict(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercises 3**: \n",
    "\n",
    "As the score suggests, now we have the perfect regression. Change the values of $y$ slightly and see what effect it has on the `mlr`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id = \"rmhp\"></a>\n",
    "\n",
    "\n",
    "### <span style=\"color:#0b486b\">2.2 Regression for median house prices</span>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are going to use the package `pandas` for reading and storing the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r",
      "  0% [                                                                              ]     0 / 20865\r",
      " 39% [..............................                                                ]  8192 / 20865\r",
      " 78% [.............................................................                 ] 16384 / 20865\r",
      "100% [..............................................................................] 20865 / 20865"
     ]
    }
   ],
   "source": [
    "#No need to use wget if you've retrieved file from clouddeakin.\n",
    "wget.download('https://raw.githubusercontent.com/gaoshangdeakin/SIT384/master/housing_300.csv')\n",
    "\n",
    "data = pd.read_csv('housing_300.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>MEDV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1</td>\n",
       "      <td>296</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD  TAX  PTRATIO  \\\n",
       "0  0.00632  18.0   2.31     0  0.538  6.575  65.2  4.0900    1  296     15.3   \n",
       "1  0.02731   0.0   7.07     0  0.469  6.421  78.9  4.9671    2  242     17.8   \n",
       "2  0.02729   0.0   7.07     0  0.469  7.185  61.1  4.9671    2  242     17.8   \n",
       "3  0.03237   0.0   2.18     0  0.458  6.998  45.8  6.0622    3  222     18.7   \n",
       "4  0.06905   0.0   2.18     0  0.458  7.147  54.2  6.0622    3  222     18.7   \n",
       "\n",
       "        B  LSTAT  MEDV  \n",
       "0  396.90   4.98  24.0  \n",
       "1  396.90   9.14  21.6  \n",
       "2  392.83   4.03  34.7  \n",
       "3  394.63   2.94  33.4  \n",
       "4  396.90   5.33  36.2  "
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>MEDV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>count</td>\n",
       "      <td>300.000000</td>\n",
       "      <td>300.000000</td>\n",
       "      <td>300.000000</td>\n",
       "      <td>300.00000</td>\n",
       "      <td>300.000000</td>\n",
       "      <td>300.000000</td>\n",
       "      <td>300.000000</td>\n",
       "      <td>300.000000</td>\n",
       "      <td>300.000000</td>\n",
       "      <td>300.000000</td>\n",
       "      <td>300.000000</td>\n",
       "      <td>300.000000</td>\n",
       "      <td>300.000000</td>\n",
       "      <td>300.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mean</td>\n",
       "      <td>0.435446</td>\n",
       "      <td>15.386667</td>\n",
       "      <td>8.873600</td>\n",
       "      <td>0.09000</td>\n",
       "      <td>0.514333</td>\n",
       "      <td>6.420333</td>\n",
       "      <td>62.796667</td>\n",
       "      <td>4.279012</td>\n",
       "      <td>4.486667</td>\n",
       "      <td>312.043333</td>\n",
       "      <td>17.588333</td>\n",
       "      <td>378.708600</td>\n",
       "      <td>10.704167</td>\n",
       "      <td>25.484667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>std</td>\n",
       "      <td>0.670445</td>\n",
       "      <td>25.968217</td>\n",
       "      <td>6.378924</td>\n",
       "      <td>0.28666</td>\n",
       "      <td>0.108867</td>\n",
       "      <td>0.706043</td>\n",
       "      <td>29.141200</td>\n",
       "      <td>1.980475</td>\n",
       "      <td>1.618194</td>\n",
       "      <td>69.105717</td>\n",
       "      <td>2.286012</td>\n",
       "      <td>43.328929</td>\n",
       "      <td>6.208806</td>\n",
       "      <td>8.887553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>min</td>\n",
       "      <td>0.006320</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.460000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.385000</td>\n",
       "      <td>4.903000</td>\n",
       "      <td>2.900000</td>\n",
       "      <td>1.321600</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>188.000000</td>\n",
       "      <td>12.600000</td>\n",
       "      <td>70.800000</td>\n",
       "      <td>1.730000</td>\n",
       "      <td>11.800000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>25%</td>\n",
       "      <td>0.068810</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.050000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.437000</td>\n",
       "      <td>5.934500</td>\n",
       "      <td>36.600000</td>\n",
       "      <td>2.597450</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>264.000000</td>\n",
       "      <td>15.600000</td>\n",
       "      <td>381.075000</td>\n",
       "      <td>5.907500</td>\n",
       "      <td>19.575000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>50%</td>\n",
       "      <td>0.139950</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6.660000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.489000</td>\n",
       "      <td>6.249500</td>\n",
       "      <td>66.800000</td>\n",
       "      <td>3.945400</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>307.000000</td>\n",
       "      <td>17.800000</td>\n",
       "      <td>392.215000</td>\n",
       "      <td>9.530000</td>\n",
       "      <td>23.100000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>75%</td>\n",
       "      <td>0.522168</td>\n",
       "      <td>21.250000</td>\n",
       "      <td>10.590000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.547000</td>\n",
       "      <td>6.781250</td>\n",
       "      <td>91.350000</td>\n",
       "      <td>5.720900</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>384.000000</td>\n",
       "      <td>19.100000</td>\n",
       "      <td>395.622500</td>\n",
       "      <td>14.112500</td>\n",
       "      <td>29.650000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>max</td>\n",
       "      <td>4.097400</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>25.650000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>0.871000</td>\n",
       "      <td>8.725000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>9.222900</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>469.000000</td>\n",
       "      <td>21.200000</td>\n",
       "      <td>396.900000</td>\n",
       "      <td>34.410000</td>\n",
       "      <td>50.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             CRIM          ZN       INDUS       CHAS         NOX          RM  \\\n",
       "count  300.000000  300.000000  300.000000  300.00000  300.000000  300.000000   \n",
       "mean     0.435446   15.386667    8.873600    0.09000    0.514333    6.420333   \n",
       "std      0.670445   25.968217    6.378924    0.28666    0.108867    0.706043   \n",
       "min      0.006320    0.000000    0.460000    0.00000    0.385000    4.903000   \n",
       "25%      0.068810    0.000000    4.050000    0.00000    0.437000    5.934500   \n",
       "50%      0.139950    0.000000    6.660000    0.00000    0.489000    6.249500   \n",
       "75%      0.522168   21.250000   10.590000    0.00000    0.547000    6.781250   \n",
       "max      4.097400  100.000000   25.650000    1.00000    0.871000    8.725000   \n",
       "\n",
       "              AGE         DIS         RAD         TAX     PTRATIO           B  \\\n",
       "count  300.000000  300.000000  300.000000  300.000000  300.000000  300.000000   \n",
       "mean    62.796667    4.279012    4.486667  312.043333   17.588333  378.708600   \n",
       "std     29.141200    1.980475    1.618194   69.105717    2.286012   43.328929   \n",
       "min      2.900000    1.321600    1.000000  188.000000   12.600000   70.800000   \n",
       "25%     36.600000    2.597450    4.000000  264.000000   15.600000  381.075000   \n",
       "50%     66.800000    3.945400    4.000000  307.000000   17.800000  392.215000   \n",
       "75%     91.350000    5.720900    5.000000  384.000000   19.100000  395.622500   \n",
       "max    100.000000    9.222900    8.000000  469.000000   21.200000  396.900000   \n",
       "\n",
       "            LSTAT        MEDV  \n",
       "count  300.000000  300.000000  \n",
       "mean    10.704167   25.484667  \n",
       "std      6.208806    8.887553  \n",
       "min      1.730000   11.800000  \n",
       "25%      5.907500   19.575000  \n",
       "50%      9.530000   23.100000  \n",
       "75%     14.112500   29.650000  \n",
       "max     34.410000   50.000000  "
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the scatter plot of the number of rooms vs the median house prices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$Y$ (median house prices)')"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7, 7), dpi=100)\n",
    "median_prices = data['MEDV']\n",
    "avg_rooms = data['RM']\n",
    "#ones() function returns a new array of given shape and data type, where the element's value is set to 1.\n",
    "#https://www.geeksforgeeks.org/numpy-ones-python/ \n",
    "scales = 50*np.ones(len(median_prices))\n",
    "ax.scatter(avg_rooms, median_prices, color='b',s=scales, alpha=0.7, edgecolor='r')\n",
    "plt.xlabel('$X$ (number of rooms)')\n",
    "plt.ylabel('$Y$ (median house prices)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "avg_rooms.shape: (300,)\n",
      "median_prices.shape: (300,)\n"
     ]
    }
   ],
   "source": [
    "print (\"avg_rooms.shape:\", avg_rooms.shape)\n",
    "print (\"median_prices.shape:\", median_prices.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How correlated are the number of rooms and the price of the house?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.89804265],\n",
       "       [0.89804265, 1.        ]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(avg_rooms, median_prices)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we want to fit a linear regression mode on the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# prepare the data\n",
    "\n",
    "x = np.c_[avg_rooms.values]\n",
    "y = median_prices.tolist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import linear_model\n",
    "lr = linear_model.LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.fit(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[11.30440747]\n",
      "-47.09339739688137\n"
     ]
    }
   ],
   "source": [
    "print (lr.coef_)\n",
    "print (lr.intercept_)\n",
    "# print lr.residues_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[11.30440747] -47.09339739688137\n"
     ]
    }
   ],
   "source": [
    "# obtain the model parameters\n",
    "\n",
    "print (lr.coef_, lr.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "# predict \n",
    "\n",
    "yhat = lr.predict(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x[:10]: [[6.575]\n",
      " [6.421]\n",
      " [7.185]\n",
      " [6.998]\n",
      " [7.147]\n",
      " [6.43 ]\n",
      " [6.012]\n",
      " [6.172]\n",
      " [5.631]\n",
      " [6.004]]\n",
      "yhat[:10]: [27.23308169 25.49220294 34.12877024 32.01484605 33.69920276 25.59394261\n",
      " 20.86870028 22.67740548 16.56172104 20.77826503]\n"
     ]
    }
   ],
   "source": [
    "print (\"x[:10]:\", x[:10])\n",
    "print (\"yhat[:10]:\", yhat[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot the result\n",
    "\n",
    "fig,ax = plt.subplots(figsize=(7,7),dpi=100)\n",
    "\n",
    "scales = 20*np.ones(len(median_prices))\n",
    "\n",
    "#s: marker size; color: marker color; alpha: marker opacity.\n",
    "#e.g. ax.scatter(x, y, s=10)\n",
    "#https://problemsolvingwithpython.com/06-Plotting-with-Matplotlib/06.10-Scatter-Plots/\n",
    "ax.scatter(avg_rooms,median_prices,color='b',s=scales,alpha=0.7,edgecolor='r')\n",
    "\n",
    "#ax set methods can also be used\n",
    "#ax.set_title('xxxx')\n",
    "#ax.set_xlabel('$X$ (number of rooms)')\n",
    "#ax.set_ylabel('$Y$ (median house prices)')\n",
    "plt.xlabel('$X$ (number of rooms)')\n",
    "plt.ylabel('$Y$ (median house prices)')\n",
    "\n",
    "# plot the regression linear leared\n",
    "ax.plot(x,yhat)\n",
    "#ax.scatter(x,yhat,color='r',s=scales,alpha=0.7,edgecolor='g') #scatter the x and predicted y\n",
    "\n",
    "# visualize the residuals\n",
    "\n",
    "#reshape() function is used to give a new shape to an array without changing its data.\n",
    "#numpy.reshape(arr, new_shape, order)\n",
    "#useful links: \n",
    "#https://www.w3resource.com/numpy/manipulation/reshape.php\n",
    "#https://stackoverflow.com/questions/18691084/what-does-1-mean-in-numpy-reshape \n",
    "tmp = np.reshape(x,[1,len(x)])[0] #get all the x coordinate\n",
    "tmp_x = []\n",
    "tmp_y = []\n",
    "for i in range(len(x)): #for each x\n",
    "    tmp_x = np.append(tmp_x,tmp[i]) #get x coordinate\n",
    "    tmp_y = np.append(tmp_y,y[i]) #get y coordinate\n",
    "    tmp_x = np.append(tmp_x,tmp[i]) #get x coordinate again\n",
    "    tmp_y = np.append(tmp_y,yhat[i]) #get predicted y coordinate\n",
    "    ax.plot(tmp_x,tmp_y,color='g',linewidth=0.5) #draw vertical residual line using (x,y) and (x,predicted y)\n",
    "    tmp_x = []\n",
    "    tmp_y = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "#sum of residual\n",
    "#lr.residues_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is customary to test your model on **unseen** data. So we divide our data into two parts. We use 70% of it to train the model and 30% to evaluate its performance on unseen data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "210"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "split = 0.7\n",
    "split_idx = int(np.round(split * len(data)))\n",
    "split_idx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>MEDV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1</td>\n",
       "      <td>296</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD  TAX  PTRATIO  \\\n",
       "0  0.00632  18.0   2.31     0  0.538  6.575  65.2  4.0900    1  296     15.3   \n",
       "1  0.02731   0.0   7.07     0  0.469  6.421  78.9  4.9671    2  242     17.8   \n",
       "2  0.02729   0.0   7.07     0  0.469  7.185  61.1  4.9671    2  242     17.8   \n",
       "3  0.03237   0.0   2.18     0  0.458  6.998  45.8  6.0622    3  222     18.7   \n",
       "4  0.06905   0.0   2.18     0  0.458  7.147  54.2  6.0622    3  222     18.7   \n",
       "\n",
       "        B  LSTAT  MEDV  \n",
       "0  396.90   4.98  24.0  \n",
       "1  396.90   9.14  21.6  \n",
       "2  392.83   4.03  34.7  \n",
       "3  394.63   2.94  33.4  \n",
       "4  396.90   5.33  36.2  "
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_data = data[0:200]\n",
    "train_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1d0e44213c8>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 2, sharey=True)\n",
    "train_data.plot(kind='scatter', x='RM', y='MEDV', ax=axs[0], figsize=(7, 7))\n",
    "train_data.plot(kind='scatter', x='AGE', y='MEDV', ax=axs[1], figsize=(7, 7))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>MEDV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>200</td>\n",
       "      <td>0.01778</td>\n",
       "      <td>95.0</td>\n",
       "      <td>1.47</td>\n",
       "      <td>0</td>\n",
       "      <td>0.4030</td>\n",
       "      <td>7.135</td>\n",
       "      <td>13.9</td>\n",
       "      <td>7.6534</td>\n",
       "      <td>3</td>\n",
       "      <td>402</td>\n",
       "      <td>17.0</td>\n",
       "      <td>384.30</td>\n",
       "      <td>4.45</td>\n",
       "      <td>32.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>201</td>\n",
       "      <td>0.03445</td>\n",
       "      <td>82.5</td>\n",
       "      <td>2.03</td>\n",
       "      <td>0</td>\n",
       "      <td>0.4150</td>\n",
       "      <td>6.162</td>\n",
       "      <td>38.4</td>\n",
       "      <td>6.2700</td>\n",
       "      <td>2</td>\n",
       "      <td>348</td>\n",
       "      <td>14.7</td>\n",
       "      <td>393.77</td>\n",
       "      <td>7.43</td>\n",
       "      <td>24.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>202</td>\n",
       "      <td>0.02177</td>\n",
       "      <td>82.5</td>\n",
       "      <td>2.03</td>\n",
       "      <td>0</td>\n",
       "      <td>0.4150</td>\n",
       "      <td>7.610</td>\n",
       "      <td>15.7</td>\n",
       "      <td>6.2700</td>\n",
       "      <td>2</td>\n",
       "      <td>348</td>\n",
       "      <td>14.7</td>\n",
       "      <td>395.38</td>\n",
       "      <td>3.11</td>\n",
       "      <td>42.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>203</td>\n",
       "      <td>0.03510</td>\n",
       "      <td>95.0</td>\n",
       "      <td>2.68</td>\n",
       "      <td>0</td>\n",
       "      <td>0.4161</td>\n",
       "      <td>7.853</td>\n",
       "      <td>33.2</td>\n",
       "      <td>5.1180</td>\n",
       "      <td>4</td>\n",
       "      <td>224</td>\n",
       "      <td>14.7</td>\n",
       "      <td>392.78</td>\n",
       "      <td>3.81</td>\n",
       "      <td>48.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>204</td>\n",
       "      <td>0.02009</td>\n",
       "      <td>95.0</td>\n",
       "      <td>2.68</td>\n",
       "      <td>0</td>\n",
       "      <td>0.4161</td>\n",
       "      <td>8.034</td>\n",
       "      <td>31.9</td>\n",
       "      <td>5.1180</td>\n",
       "      <td>4</td>\n",
       "      <td>224</td>\n",
       "      <td>14.7</td>\n",
       "      <td>390.55</td>\n",
       "      <td>2.88</td>\n",
       "      <td>50.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        CRIM    ZN  INDUS  CHAS     NOX     RM   AGE     DIS  RAD  TAX  \\\n",
       "200  0.01778  95.0   1.47     0  0.4030  7.135  13.9  7.6534    3  402   \n",
       "201  0.03445  82.5   2.03     0  0.4150  6.162  38.4  6.2700    2  348   \n",
       "202  0.02177  82.5   2.03     0  0.4150  7.610  15.7  6.2700    2  348   \n",
       "203  0.03510  95.0   2.68     0  0.4161  7.853  33.2  5.1180    4  224   \n",
       "204  0.02009  95.0   2.68     0  0.4161  8.034  31.9  5.1180    4  224   \n",
       "\n",
       "     PTRATIO       B  LSTAT  MEDV  \n",
       "200     17.0  384.30   4.45  32.9  \n",
       "201     14.7  393.77   7.43  24.1  \n",
       "202     14.7  395.38   3.11  42.3  \n",
       "203     14.7  392.78   3.81  48.5  \n",
       "204     14.7  390.55   2.88  50.0  "
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_data = data[200:300]\n",
    "test_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_X = train_data['RM'].values\n",
    "train_X = np.c_[train_X]\n",
    "train_Y = train_data['MEDV'].tolist()\n",
    "\n",
    "test_X = test_data['RM'].values\n",
    "test_X = np.c_[test_X]\n",
    "test_Y = test_data['MEDV'].tolist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'>\n",
      "(200, 1)\n",
      "<class 'list'>\n"
     ]
    }
   ],
   "source": [
    "print (type(train_X))\n",
    "print (train_X.shape)\n",
    "print (type(train_Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''\n",
    "Build a linear regression model from training data\n",
    "'''\n",
    "from sklearn import linear_model\n",
    "lr = linear_model.LinearRegression()\n",
    "\n",
    "lr.fit(train_X, train_Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[11.48585853]\n",
      "-48.553067034025624\n"
     ]
    }
   ],
   "source": [
    "print (lr.coef_)\n",
    "print (lr.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we plot the linear regression result and the data to see how it fits the training data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1d0e428de88>]"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(figsize=(7,7),dpi=100)\n",
    "\n",
    "# plot training data\n",
    "scales = 20*np.ones(len(train_Y))\n",
    "ax.scatter(train_X,train_Y,color='b',s=scales,alpha=0.7,edgecolor='r')\n",
    "plt.xlabel('$X$ (number of rooms)')\n",
    "plt.ylabel('$Y$ (median house prices)')\n",
    "plt.title('Training a simple linear regression model')\n",
    "\n",
    "# plot the regression line\n",
    "train_Yhat = lr.predict(train_X)\n",
    "plt.plot(train_X,train_Yhat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have obtained the model parameters, we can use the model to predict for unseen data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "yhat_test = lr.predict(test_X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(figsize=(7,7),dpi=100)\n",
    "\n",
    "# plot the predicted points along the prediction line\n",
    "scales = 30*np.ones(len(test_X))\n",
    "ax.scatter(test_X,yhat_test,s=scales,color='b',edgecolor='r') #predicted points\n",
    "ax.plot(test_X,yhat_test,color='b',linewidth=.2) #prediction line\n",
    "\n",
    "# plot the true values\n",
    "scales = 30*np.ones(len(test_X))\n",
    "ax.scatter(test_X,test_Y,s=scales,color='g',edgecolor='b') #test y: true value\n",
    "\n",
    "# plot the residual line\n",
    "# get all the x coordinate (test_X) from the test dataset\n",
    "tmp = np.reshape(test_X,[1,len(test_X)])[0]\n",
    "\n",
    "#the following print statements are for better understanding\n",
    "#print(\"test_X\", test_X)\n",
    "#print(\"np.reshape(test_X,[1,len(test_X)])\", np.reshape(test_X,[1,len(test_X)]))\n",
    "#print(\"tmp:\",tmp)\n",
    "\n",
    "tmp_x = []\n",
    "tmp_y = []\n",
    "for i in range(len(test_X)): #for each x in test set\n",
    "    tmp_x = np.append(tmp_x,tmp[i]) #get x coordinate\n",
    "    tmp_y = np.append(tmp_y,yhat_test[i]) #get predicted y coordinate\n",
    "    tmp_x = np.append(tmp_x,tmp[i]) #get x coordinate again\n",
    "    tmp_y = np.append(tmp_y,test_Y[i]) #get test y coordinate\n",
    "    ax.plot(tmp_x,tmp_y,color='red',linewidth=0.5) #draw the vertical residual line (x,yhat), (x,test_y)\n",
    "    tmp_x = []\n",
    "    tmp_y = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>MEDV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1</td>\n",
       "      <td>296</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD  TAX  PTRATIO  \\\n",
       "0  0.00632  18.0   2.31     0  0.538  6.575  65.2  4.0900    1  296     15.3   \n",
       "1  0.02731   0.0   7.07     0  0.469  6.421  78.9  4.9671    2  242     17.8   \n",
       "2  0.02729   0.0   7.07     0  0.469  7.185  61.1  4.9671    2  242     17.8   \n",
       "3  0.03237   0.0   2.18     0  0.458  6.998  45.8  6.0622    3  222     18.7   \n",
       "4  0.06905   0.0   2.18     0  0.458  7.147  54.2  6.0622    3  222     18.7   \n",
       "\n",
       "        B  LSTAT  MEDV  \n",
       "0  396.90   4.98  24.0  \n",
       "1  396.90   9.14  21.6  \n",
       "2  392.83   4.03  34.7  \n",
       "3  394.63   2.94  33.4  \n",
       "4  396.90   5.33  36.2  "
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## <span style=\"color:#0b486b\">3. Distances</span>\n",
    "\n",
    "`Distance` is a numerical description of how far apart objects are. It is a concrete way of describing what it means for elements of some space to be close or far away from each other, for example the distance between two vectors in an 2-dimensional space.\n",
    "\n",
    "Now that you have know how to represent an n-dimensional vector in Python with NumPy arrays, we will write a function as a metric to measure the distance between two vectors. There are multiple ways to measure the distance between two vectors. We will discuss Euclidean distance and cosine distance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<a id = \"euclidean\"></a>\n",
    "\n",
    "\n",
    "### <span style=\"color:#0b486b\">3.1 Euclidean Distance</span>\n",
    "\n",
    "Euclidean distance comes from Geometry. If we assume $\\mathbf{x}_{1}=\\left[x_{11},x_{12},\\ldots,x_{1n}\\right]$ and $\\mathbf{x}_{2}=\\left[x_{21},x_{22},\\ldots,x_{2n}\\right]$, then the Euclidean distance between $\\mathbf{x}_{1}$ and $\\mathbf{x}_{2}$ is defined as:\n",
    "\n",
    "$$d\\left(\\mathbf{x}_{1},\\mathbf{x}_{2}\\right)=\\sqrt{\\left(x_{11}-x_{21}\\right)^{2}+\\left(x_{12}-x_{22}\\right)^{2}+\\ldots+\\left(x_{1n}-x_{2n}\\right)^{2}}\n",
    "$$\n",
    "\n",
    "We can use array operators for this task."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1  0 -2 -2  2]\n",
      "[1 0 4 4 4]\n",
      "3.605551275463989\n"
     ]
    }
   ],
   "source": [
    "x1 = np.array([2, 5, 4, 6, 8])\n",
    "x2 = np.array([3, 5, 6, 8, 6])\n",
    "\n",
    "print (x1 - x2)\n",
    "print ((x1 - x2) ** 2)\n",
    "print (np.sqrt(np.sum((x1 - x2) ** 2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "def euclidean_distance1(x1, x2):\n",
    "    d = x1 - x2\n",
    "    d = d ** 2\n",
    "    return np.sqrt(d.sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.14142842854285\n"
     ]
    }
   ],
   "source": [
    "x1 = np.array([-1, 2, 0, 5])\n",
    "x2 = np.array([4, 2, 1, 0])\n",
    "\n",
    "print (euclidean_distance1(x1, x2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since two vectors passed to the function should be the same size, it is better to perform a sanity check before applying the subtraction. Otherwise it will raise an error. We can do this by using `if - elif` statement or as a better practice by using `try - except`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "\n",
    "def euclidean_distance2(x1, x2):\n",
    "    if x1.shape[0] != x2.shape[0]:\n",
    "        sys.exit('x1 and x2 are not the same size')\n",
    "    else:\n",
    "        d = x1 - x2\n",
    "        d = d ** 2\n",
    "        return np.sqrt(d.sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.723805294763608"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fix this cell\n",
    "\n",
    "x1 = np.array([-1, 2, 0, 5, 9])\n",
    "x2 = np.array([4, 2, 1, 0, 1])\n",
    "euclidean_distance2(x1, x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "def euclidean_distance3(x1, x2):\n",
    "    try:\n",
    "        d = x1 - x2\n",
    "        d = np.power(d, 2)\n",
    "        return np.sqrt(d.sum())\n",
    "    except ValueError as e:\n",
    "        print (\"Vectors passed to the function are not the same size\")\n",
    "        # you can return a default value\n",
    "        return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vectors passed to the function are not the same size\n"
     ]
    }
   ],
   "source": [
    "# fix this cell\n",
    "\n",
    "x1 = np.array([-1, 2, 0, 5, 9])\n",
    "x2 = np.array([4, 2, 1, 2])\n",
    "a = euclidean_distance3(x1, x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "def euclidean_distance4(x1, x2):\n",
    "    try:\n",
    "        d = np.array(x1) - np.array(x2)\n",
    "        d = np.power(d, 2)\n",
    "        return np.sqrt(d.sum())\n",
    "    except ValueError as e:\n",
    "        print (\"Vectors passed to the function are not the same size\")\n",
    "        # you can return a default value\n",
    "        return None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id = \"cosine\"></a>\n",
    "\n",
    "### <span style=\"color:#0b486b\">3.2 cosine similarity and distance</span>\n",
    "\n",
    "Cosine similarity is a measure of similarity between two vectors based on the angle between them. Cosine similarity is widely used in information retrieval and text mining as a measure of similarity between documents and is defined as:\n",
    "\n",
    "$$S_{c}\\left(\\mathbf{x}_{1},\\mathbf{x_{2}}\\right)=\\frac{\\mathbf{x}_{1}.\\mathbf{x_{2}}}{\\parallel\\mathbf{x}_{1}\\parallel^{2}+\\parallel\\mathbf{x}_{2}\\parallel^{2}-\\mathbf{x}_{1}.\\mathbf{x_{2}}}$$\n",
    "\n",
    "\n",
    "Cosine similarity is particularly used in positive space where the outcome is bounded in [0, 1]. The cosine distance is defined as the complement to cosine similarity in positive space that is $D_{c}\\left(x_{1},x_{2}\\right)=1-S_{c}\\left(x_1,x_2\\right)$ where $D_c$ is the cosine distance and $S_c$ is the cosine similarity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 4 9]\n"
     ]
    }
   ],
   "source": [
    "x1 = np.array([1,2,3])\n",
    "x2 = np.array([3,4,6])\n",
    "\n",
    "print(x1 * x1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cosine_distance(x1, x2):\n",
    "    try:\n",
    "        num = (x1*x2).sum()\n",
    "        denom = (x1*x1).sum() + (x2*x2).sum() - (x1*x2).sum()\n",
    "        num += 0.0    # or use np.astype(float) to make sure of float division\n",
    "        return 1 - num/denom\n",
    "    except ValueError as e:\n",
    "        print (\"Vectors passed to the function are not the same size\")\n",
    "        return None\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8898305084745762"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1 = np.array([2, 0, 5, 9])\n",
    "x2 = np.array([4, 2, 1, 0])\n",
    "cosine_distance(x1, x2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <span style=\"color:#0b486b\">Tasks</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Try the provided examples and get yourself familiar with sample plot code before attempting portolio tasks.\n",
    "\n",
    "Please show your attempt to your tutor before you leave the lab, or email your files to your coordinator if you are an off-campus student."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <span style=\"color:#0b486b\">Summary</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this session we have covered: \n",
    " - data dependency, linear regression and distances.\n",
    " - how to apply linear regression in Python."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reference:\n",
    "1. Yash Soni, \"Machine Learning for dummies — explained in 3 mins!\", https://becominghuman.ai/machine-learning-for-dummies-explained-in-2-mins-e83fbc55ac6d, accessed 31/03/2019."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
